Deep inside an abandoned temple, Emek and Luna encountered a series of mirror gates, each controlled by a transformed geometric symbol. To open a gate, they had to determine whether the symbol had been translated, rotated, or reflected from the original design. Before activating each mechanism, they verified that the chosen transformation preserved the figure's size and shape while matching its new position or orientation. Their careful reasoning prevented costly mistakes, unlocked every gate in sequence, and finally revealed the expedition's long-lost map hidden within the final chamber.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Compare how the signs of the x- and y-coordinates change.
At one mirror gate, a triangular symbol changes from points (2, 1), (5, 1), and (2, 4) to points (-2, 1), (-5, 1), and (-2, 4). Which transformation occurred?
A translation 4 units leftA reflection across the y-axisA reflection across the x-axisA 90° rotation clockwise about the originCorrect! The x-coordinates change signs while the y-coordinates stay the same.
Try again. Check which coordinate changes sign for every point.
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Hint
Multiply the angle of one rotation by the number of rotations.
A gate symbol is rotated 90° clockwise three times about its center. Through how many degrees has it rotated altogether?
Correct! Three 90° rotations total 270°.
Try again. Add 90° three times.
Next🎉 Congrats! You got this question!
Hint
Recall which properties are preserved by translations, rotations, and reflections.
Luna says a symbol was translated because its position changed, but its orientation stayed the same. Emek notices that the image is also larger than the original. Which conclusion is correct?
Luna is correct because every translation changes size.Luna is correct because position is the only feature that matters.Luna is incorrect because a translation preserves both size and shape.Luna is incorrect because a translation must reverse orientation.Correct! A translation cannot make a figure larger.
Try again. Rigid transformations preserve the figure's size and shape.
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